Stability of constant equilibrium state for dissipative balance laws system with a convex entropy

Ruggeri, Tommaso; Serre, Denis

doi:10.1090/qam/2032577

Authors: Tommaso Ruggeri and Denis Serre
Journal: Quart. Appl. Math. 62 (2004), 163-179
MSC: Primary 35L65; Secondary 35B35, 35L60, 82C05
DOI: https://doi.org/10.1090/qam/2032577
MathSciNet review: MR2032577
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Abstract: For a one-dimensional system of dissipative balance laws endowed with a convex entropy, we prove, under natural assumptions, that a constant equilibrium state is asymptotically ${L^2}$-stable under a zero-mass initial disturbance. The technique is based on the construction of an appropriate Liapunov functional involving the entropy and a so-called compensation term.

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